Question

How long will it take to John to double his deposit of $\$500$ at $9\%$ simple interest?

Answer 1

Hint: In this question, we have to find the time taken by John’s amount to double. Thus, we will use the simple interest formula to get the solution. Now, we know that the simple interest is equal the multiplication of the principal amount, the rate of interest and the time taken, divided by 100, that is $\text{simple interest amount }=\dfrac{\text{principal amount}\times \left( \text{rate of interest} \right)\%\times \text{time}}{100}$ . So, in this problem, principal amount is equal to $\$500$ , rate of interest is equal to $9\%$ , time is equal to $t$ , and the simple interest amount is equal to $I=P=\$500$ . Thus, we will substitute these values in the above formula. After that, we will make the necessary calculations using mathematical operations, to get the accurate solution.

Complete step-by-step answer:
According to the question, we have to find the number of years taken by John’s amount to double.
Thus, we will use the simple interest formula to get the solution.
As we know, the simple interest formula s equal to $\text{simple interest amount }=\dfrac{\text{principal amount}\times \left( \text{rate of interest} \right)\text{ }\!\!\%\!\!\text{ }\times \text{time}}{100}$ --------- (1)
Where, the principal amount is equal to $\$500$ ---------- (2)
The rate of interest is equal to $9\%$ ---------- (3)
The time taken by amount to double is equal to $t$ ---------- (4)
And, the simple interest amount is equal to $I=P=\$500$ ----------- (5)
Thus, we will substitute the value of equation (2), (3), (4), and (5) in equation (1), we get
$\Rightarrow \$500=\dfrac{\$500\times9\%\times t}{100}$
On further solving the above equation, we get
$\Rightarrow \$500=\dfrac{\$5\times9\%\times t}{1}$
$\Rightarrow 500=\dfrac{45\times t}{1}$
Now, we will divide 45 on both sides in the above equation, we get
$\Rightarrow \dfrac{500}{45}=\dfrac{45\times t}{45}$
Thus, we get
$\Rightarrow \dfrac{500}{45}=t$
$\Rightarrow t=11.11\text{ years}$
Therefore, the time taken to John to double his deposit of $\$500$ at $9\%$ simple interest is equal to 11.11 years.

Note: While solving this problem, do mention all the steps properly to avoid confusion and mathematical errors. Do mention the simple interest formula and also mention the units of all the expressions, to get an accurate solution.